AAS 20-560 GUIDANCE, NAVIGATION, AND CONTROL FOR THE DWARF FORMATION-FLYING MISSION Vincent Giralo,∗ Michelle Chernick,y Simone D’Amicoz The Demonstration with Nanosatellites of Autonomous Rendezvous and Formation- Flying (DWARF) mission consists of a pair of identical 3U CubeSats which will act as a spaceborne testbed to further advance, rigorously validate, and embed new relative navigation and control technologies in order to meet the needs of future distributed space systems. This paper focuses on the design and implementation of the DWARF on-board Guidance, Navigation, and Control (GNC) system. The DWARF mission will demonstrate unprecedented real-time centimeter-level nav- igation accuracy on board and new safe, robust, and autonomous relative orbit control algorithms. INTRODUCTION Distributed space systems (DSS) employ multiple co-orbiting units to enable advanced missions in space science, technology, and infrastructure. As mission concepts become more complex, fu- ture space architectures must address new challenges in relative navigation and control accuracy, robustness, and safety. The Demonstration with Nanosatellites of Autonomous Rendezvous and Formation-Flying (DWARF) mission, developed by the Stanford Space Rendezvous Laboratory (SLAB) in collaboration with Gauss S.R.L. and King Abdulaziz City for Science and Technology (KACST), seeks to demonstrate advancements in relative navigation and control to meet the needs of future ambitious distributed space systems. The on-board dedicated Guidance, Navigation, and Control (GNC) payload consists of software developed by SLAB and is integrated on two identi- cal and autonomous 3U CubeSats using commercial-off-the-shelf (COTS) hardware and a cold-gas propulsion system. The satellites, which are scheduled to launch in the first quarter of 2022, will fly in a LEO sun-synchronous orbit. Both spacecraft can assume the role of chief and deputy in order to balance fuel consumption and double the mission lifetime. The GNC software is split into two inte- grated modules, navigation and control. The navigation module employs carrier-phase differential Global Navigation Satellite System (GNSS) techniques to demonstrate real-time centimeter-level precision through the use of Integer Ambiguity Resolution (IAR) on board in the presence of fre- quent control maneuvers. The control module will perform safe, robust, and autonomous formation acquisition, keeping, and reconfiguration at separations between 100 meters and 100 kilometers. These capabilities will be demonstrated in flight for the first time, enabling future missions such as ∗Doctoral Candidate, Stanford University, Department of Aeronautics and Astronautics, Space Rendezvous Laboratory, Durand Building, 496 Lomita Mall, Stanford, CA 94305-4035 yDoctoral Candidate, Stanford University, Department of Aeronautics and Astronautics, Space Rendezvous Laboratory, Durand Building, 496 Lomita Mall, Stanford, CA 94305-4035 zAssistant Professor, Stanford University, Department of Aeronautics and Astronautics, Space Rendezvous Laboratory, Durand Building, 496 Lomita Mall, Stanford, CA 94305-4035 1 virtual telescopes,1,2 optical interferometers,3 on-orbit servicers for lifetime prolongation4 and as- sembly of larger structures in space.5 Specifically, these technologies have been identified by NASA and NSF as enablers for missions such as Starling,6–8 a swarm of four CubeSats demonstrating the capability to navigate in deep space without Global Positioning System (GPS), the Miniaturized Distributed Occulter/Telescope (mDOT),9 a precise formation of two SmallSats intending to di- rectly image exoplanets and exozodii, the Space Weather Atmospheric Reconfigurable Multiscale Experiment (SWARM-EX),10 a swarm of three CubeSats that will study Earth’s upper atmosphere, and the Virtual Super-resolution Optics with Reconfigurable Swarms (VISORS),11, 12 a precise for- mation of two CubeSats that will perform solar observations of unprecedented resolution. These missions are all under study and development at SLAB and will directly benefit from the algorithms described in this paper. The concept of multiple spacecraft operating together was first demonstrated in the 1960s dur- ing the Gemini program, with advancements continuing through the Apollo program and the Space Shuttle.13 While these early demonstrations were rudimentary by current standards, they paved the way for recent spacecraft formation-flying and rendezvous missions that require more advanced autonomous navigation and control algorithms. Numerous science missions such as the Gravity Recovery and Climate Experiment (GRACE, 2002),14 the TerraSAR-X add-on for Digital Ele- vation Measurement (TanDEM-X, 2010),15 and the Magnetospheric Multiscale Mission (MMS, 2015)16, 17 used multiple spacecraft to conduct unprecedented experiments for gravity field recov- ery, synthetic aperture radar interferometry, and magnetospheric observation, respectively. Another class of formation-flying and rendezvous missions is technology demonstrations, such as PRISMA (2010),18, 19 CanX-4/5 (2014),20 and CPOD (2020).21 Advancements in DSS missions have demon- strated state-of-the-art navigation and control algorithms on board, while also moving from large, expensive spacecraft (GRACE, TanDEM-X) to smaller, cheaper nanosatellites (CanX-4/5, CPOD). Precision navigation for DSS has largely been enabled through the use of GNSS, such as GPS. GNSS-based absolute positioning accuracies of 1m have been demonstrated for a single spacecraft in real time, while relative navigation using differential GNSS (dGNSS) techniques provide greatly higher accuracy.13 By exploiting synchronous measurements from two receivers, common errors can be cancelled out, resulting in low-noise relative measurements. This technique was validated on board in real time on missions such as PRISMA, where an Extended Kalman Filter (EKF) showed precise relative positioning results of less than 10cm (3D, RMS) between two small spacecraft throughout most mission scenarios.18, 19, 22, 23 Similar results were obtained during the CanX-4/5 mission,20, 24, 25 demonstrating dGNSS for the first time on CubeSat avionics in flight. Navigation accuracies have been further improved by fixing the carrier-phase ambiguities to their integer values, a technique referred to as Integer Ambiguity Resolution. However, due to computa- tional overhead and a lack a guarantee of correctly fixing the integers, IAR has never been performed in flight. GRACE used IAR in post-processing to demonstrate 1mm (1D range-only, 1σ) relative positioning accuracy at a separation of 200km when compared with the high-precision on-board K/Ka-band ranging system.14, 26, 27 More recently, advances in spacecraft avionics have allowed for more complex algorithms such as IAR to be run on board in real time. The Distributed Multi-GNSS Timing and Localization system (DiGiTaL) is a navigation payload for nanosatellites that achieves centimeter-level positioning accuracy and nanosecond-level time synchronization throughout ar- bitrarily sized swarms.28 A reduced-dynamics estimation architecture on board each individual satellite processes low-noise measurements from multiple GNSS constellations and frequencies to reconstruct the full formation state with high accuracy. DiGiTaL demonstrated successful IAR to 2 provide less than 1cm (1D, RMS) of relative positioning accuracy in real time for a swarm of four spacecraft over short baselines using full CubeSat avionics in the loop.29 The system was developed by SLAB in cooperation with Goddard Space Flight Center and Tyvak Nanosatellite Systems as part of the NASA Small Spacecraft Technology Program (SSTP). The DWARF mission will be the first in-flight demonstration of both DiGiTaL and online IAR. Advancements have also been made to push towards robust and autonomous control of spacecraft relative motion. An on-board relative control software aims to minimize the delta-v cost of a set of impulsive control actions while achieving a desired relative state in fixed time. Recent flight demon- strations of control software such as the Spaceborne Autonomous Formation Flying Experiment (SAFE) on PRISMA30 and the TanDEM-X Autonomous Formation Flying (TAFF) system15 cast the relative orbit reconfiguration problem into quasi-nonsingular relative orbit element (ROE) space. Use of the ROE state representation overcomes the limitations of the Cartesian-based linear models of relative dynamics like the Hill-Clohessy-Wiltshire equations (HCW) and Yamanaka-Ankerson (YA) equations, which are accurate only for small spacecraft separations. The ROE state allows for linearization of the equations that govern relative motion with minimal loss of accuracy. In addition, use of the ROE state provides a geometric intuition that can be exploited to derive simple geometric conditions for collision avoidance and safety, called relative eccentricity/inclina- tion (E/I) vector separation.22 Typically, mission designers maintain safe separation using a relative spacecraft configuration called the safety ellipse,31 which is defined such that the relative motion in the radial-tangential/radial-normal (RT/RN) planes is bounded and periodic. The OSAM-1 (for- merly Restore-L) mission, set to launch in 2020, plans to use safety ellipses in their approach tra- jectory.4 However, D’Amico et al. showed that the minimum separation between the spacecraft over several orbits can be expressed analytically as a function of the ROE, and derived simple ex- pressions for the relationship between the relative eccentricity